There is an unbalanced coin. If you flip it you could get the probability of head P(head) = 0.6 and tail P(tail) = 0.4. Then how can we use it to predict an event that would happen with a probability of 0.5?

Jiafeng L.

Answer:

Because the coin is not balanced, you cannot get a 0.5 probability in only one flip. Then you could think about flip it twice, and there are 4 cases totally: {head,head},{head,tail},{tail,head},{tail,tail}. Calculate the joint probability of each case: P[head,head] = 0.6*0.6 = 0.36, P[head,tail] = P[tail,head] = 0.6 * 0.4 = 0.24, P[tail,tail] = 0.4 * 0.4 = 0.16. Since probabilities of case {head,tail}, {tail,head} are equal, we could only keep these two case to predict the given event and throw the other cases. So we could define case {head,tail} for the event would happen and {tail,head} for the event would not happen.

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